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In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex. There are 35 unique heptellations for the 8-simplex, including all permutations of runcations, cantellations, runcinations, sterications, pentellations, and hexications. The simplest heptellated 8-simplex is also called an expanded 8-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 8-simplex. The highest form, the heptihexipentisteriruncicantitruncated 8-simplex is more simply called a omnitruncated 8-simplex with all of the nodes ringed.

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• Heptellated 8-simplexes
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• In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex. There are 35 unique heptellations for the 8-simplex, including all permutations of runcations, cantellations, runcinations, sterications, pentellations, and hexications. The simplest heptellated 8-simplex is also called an expanded 8-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 8-simplex. The highest form, the heptihexipentisteriruncicantitruncated 8-simplex is more simply called a omnitruncated 8-simplex with all of the nodes ringed.
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• In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex. There are 35 unique heptellations for the 8-simplex, including all permutations of runcations, cantellations, runcinations, sterications, pentellations, and hexications. The simplest heptellated 8-simplex is also called an expanded 8-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 8-simplex. The highest form, the heptihexipentisteriruncicantitruncated 8-simplex is more simply called a omnitruncated 8-simplex with all of the nodes ringed.
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